Recent content by johnshade

The Halmos book is a good rec. His mission statement is summed up in the last few sentences of his introduction: "In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some and here it is; read it, absorb it, and forget it."

Halmos is superb, a little terse but very clear. Also good, and cheaper, is the Dover book by Patrick Suppes, Axiomatic set theory.

I don't know if there's an online source for this, but Patrick Suppes' book Axiomatic Set Theory, which is an inexpensive Dover paperback, has a nice clear treatment of the construction of the reals. https://www.amazon.com/dp/0486616304/?tag=pfamazon01-20

The Disquisitiones Arithmeticae is available in English: https://www.amazon.com/dp/0387962549/?tag=pfamazon01-20

This algebra book has also gotten good reviews and I've just ordered it. I have a kid who's been struggling a bit with algebra and I'm looking at it to see if I can use it to help make clear the whys and wherefores (and therefores!). Algebra by I.M. Gelfand, Alexander Shen ISBN #0817636773...

I also learned from Fraleigh many years ago and found it clear and to the point.

The big fat pi is the product analogue to the big fat sigma for sums. Suppose for example that k=3 and n1= 2, n2=3, n3=5. Then the denominator of the fraction would be (2!)(3!)(5!).

Put the left-hand side over a common denominator. You're nearly there!

Remember that since B is a subset of U(S(n)), every element of B must be an element of some S(n). So if B is finite, it must be a subset of some finite union of S(n)s. And what do you know about a finite union of S(n)s where the sequence S(n) is increasing and infinite? (By the way, as the...

Try this; I think it's a possible direction. Suppose the assumption (i.e. that for every infinite subset B' of B there is some n for which B' intersect S(n) is infinite) is true, but B is not a subset of any S(N). Then for any S(n), Ex (x is an element of B but x is not an element of S(n)...

The Australian "philosopher" colin leslie dean seems to have been extremely drunk when he wrote this paper.

Wasn't that the book Ramanujan taught himself out of?

The Mileti looks good, but awfully dense as an introduction. You may want to consider the Patrick Suppes book, Axiomatic Set Theory, which is a Dover publication and which is less than $15.